The perturbative approach to structure formation has recently received a lot of attention in the literature. In such setups the final predictions for observables like the power spectrum is often derived under additional approximations such as a simplified time dependence. Here we provide all-order perturbative integral solutions for density and velocity fields in generalized cosmologies, with a direct application to clustering quintessence. We go beyond the standard results based on extending the EdS-like approximations. As an illustrative example, we apply our findings to the calculation of the one-loop power spectrum of density and momentum fields. We find corrections close to 1% in the mildly nonlinear regime of $\mathrm{\Lambda }\mathrm{CDM}$ cosmologies for the density power spectrum, while in the case of the density-momentum power spectrum effects can reach up to 1.5% for $k\sim 0.2h/\mathrm{Mpc}$.

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• Cosmology
• Dark energy
• Dark matter
• Large scale structure of the Universe